Eevee Preview Render from Python
Not direct answer, but maybe helpful if you choose the way of the viewport.
The viewport is mainly faster because the GPU pushes the image directly to the screen instead of copying it back to the cpu for colomanagement and other calculations. So using the viewport, maybe directly pipelining it to whatever other output you seek might be one of the fastest solutions possible.

More detail below, basically a question and answer to and from a blender developer:
https://youtu.be/YqOs-VwehuM?t=1175

Rough transcript:

Question: "...but along those lines I've noticed that when I try to render out the EEVEE viewport, it's
significantly slower, even if I'm just rendering out as if in the OpenGL viewport in 2.79 when I'm just 
trying to render out hte viewport settings equivalently I get significantly slower render times and if 
I'm trying to render out a significant portion of a significant frame count I can preview it at 60 fps,
but when I render it out it's something like 5 fps ..."

Answer: "...basically when you do it in the viewport it's rendered by the GPU and it's displayed directly on 
the GPU so that's fast and if you are doing a play back blast (?) in the viewport it only calculates a single
sample. So when you render to an image a lot other stuff will happen. It renders 64 samples, but that's 
not the main case that happens. What happens next is that the GPU in image is copied back to the CPU 
and on modern GPUs that's a really slow process, you can only do it 20 times per second. That's the main burden
of that. Why do we copy it back to the CPU? That's for the color-management that's for the sequencer, that's for the 
compositor."